Trying to find the integral ∫π0dθ(2+cosθ)2 by complex analysis.
I let z=exp(iθ), dz=iexp(iθ)dθ, so dθ=dziz. I am trying therefore to find the integral 12iz∮Cdz(2+z2+12z)2 I am unsure of which contour I should use, and how to proceed besides that. Could anyone help?
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